Coherent Beam Splitting by a Thin Grating

The wide use of beam splitters in quantum interferometry, attosecond metrology, modern quantum information processing, foundations of quantum mechanics, has been based on coherence of beams emerging from a beam splitter. Here we further develop the approach in which a beam splitter is regarded as a transformer of an incident wave field (photon field or matter wave field) into a field which has narrow maxima at the points along and in close vicinity of two or more particular lines. This description was derived by considering a thin grating as a model of a beam splitter for photons, atoms and molecules. It is applied to answer some questions raised in the discussions on the interpretation of wave particle duality.